Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
double hi;
double b_h(double hi2, double b1) {
  double b2, ret;
  b2 = (hi2 / hi) * (b1 / 2);
  ret = b1 - 2 * b2;
  return ret;
}
int main() {
  double base, area, seg, ang, ans;
  int i, j, k, n;
  cin >> n >> hi;
  vector<double> ara;
  base = 1.0;
  area = hi * 0.5;
  seg = area / (double)n;
  double lo, up, mid;
  lo = 0.0;
  up = hi;
  ans = 0.0;
  for (i = 0; i < n - 1; i++) {
    double lo, up, mid = 0.0;
    lo = 0.0;
    up = hi;
    if (i > 0) up = ara[i - 1];
    while (lo <= up) {
      mid = (lo + up) / 2.0;
      ans = (0.5 * (base + b_h(mid, base)) * mid);
      if (fabs(ans - seg) <= 0.000000000001) {
        base = b_h(mid, base);
        break;
      } else if ((seg - ans) > 0.000000000001) {
        lo = mid + 0.000000000001;
      } else {
        up = mid - 0.000000000001;
      }
    }
    if (i == 0)
      ara.push_back(hi - mid);
    else
      ara.push_back(ara[i - 1] - mid);
    hi = ara[i];
  }
  reverse(ara.begin(), ara.end());
  for (i = 0; i < ara.size(); i++)
    cout << fixed << setprecision(12) << ara[i] << " ";
}